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DIGITAL IMAGE PROCESSING

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OORUL ISLAM COLLEGE OF ENGG, Kumaracoil
DEPARTMENT OF ECE
2 MARKS & QUESTION- ANSWERS
EC 1009 - Digital Image Processing
Class : S7 ECE
Prepared by : N.Santhi ,AP/ECE
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UNIT I – DIGITAL IMAGE FUNDAMENTALS
1. Define Image?
An Image may be defined as a two dimensional function f(x,y) where x & y are
spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x,y) is
called intensity or gray level of the image at that point. When x,y and the amplitude
values of f are all finite, discrete quantities we call the image as Digital Image.
2. Define Image Sampling?
Digitization of spatial coordinates (x,y) is called Image Sampling. To be suitable
for computer processing, an image function f(x,y) must be digitized both spatially and in
magnitude.
3. Define Quantization?
Digitizing the amplitude values is called Quantization. Quality of digital image is
determined to a large degree by the number of samples and discrete gray levels used in
sampling and quantization.
4. What is Dynamic Range?
The range of values spanned by the gray scale is called dynamic range of an
image. Image will have high contrast, if the dynamic range is high and image will have
dull washed out gray look if the dynamic range is low.
5. Define Mach band effect?
The spatial interaction of Luminance from an object and its surround creates a
phenomenon called the mach band effect.
6. Define Brightness?
Brightness of an object is the perceived luminance of the surround. Two objects
with different surroundings would have identical luminance but different brightness.
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7. Define Tapered Quantization?
If gray levels in a certain range occur frequently while others occurs rarely, the
quantization levels are finely spaced in this range and coarsely spaced outside of it.
This method is sometimes called Tapered Quantization.
8. What do you meant by Gray level?
Gray level refers to a scalar measure of intensity that ranges from black to grays
and finally to white.
9. What do you meant by Color model?
A Color model is a specification of 3D-coordinates system and a subspace within
that system where each color is represented by a single point.
10. List the hardware oriented color models?
1. RGB model
2. CMY model
3. YIQ model
4. HSI model
11. What is Hue of saturation?
Hue is a color attribute that describes a pure color where saturation gives a
measure of the degree to which a pure color is diluted by white light.
12. List the applications of color models?
1. RGB model--- used for color monitor & color video camera
2. CMY model---used for color printing
3. HIS model----used for color image processing
4. YIQ model---used for color picture transmission
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13. What is Chromatic Adoption?
` The hue of a perceived color depends on the adoption of the viewer. For
example, the American Flag will not immediately appear red, white, and blue of the
viewer has been subjected to high intensity red light before viewing the flag. The color
of the flag will appear to shift in hue toward the red component cyan.
14. Define Resolutions?
Resolution is defined as the smallest number of discernible detail in an image.
Spatial resolution is the smallest discernible>
19. Define the term Radiance?
Radiance is the total amount of energy that flows from the light source, and it is
usually measured in watts (w).
20. Define the term Luminance?
Luminance measured in lumens (lm), gives a measure of the amount of energy
an observer perceiver from a light source.
21. What is Image Transform?
An image can be expanded in terms of a discrete set of basis arrays called basis
images. These basis images can be generated by unitary matrices. Alternatively, a
given NXN image can be viewed as an N^2X1 vectors. An image transform provides a
set of coordinates or basis vectors for vector space.
22. What are the applications of transform.
1) To reduce band width
2) To reduce redundancy
3) To extract feature.
23. Give the Conditions for perfect transform?
Transpose of matrix = Inverse of a matrix.
Orthoganality.
24. What are the properties of unitary transform?
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1) Determinant and the Eigen values of a unitary matrix have unity magnitude
2) the entropy of a random vector is preserved under a unitary Transformation
3) Since the entropy is a measure of average information, this means information
is preserved under a unitary transformation.
25. Write the expression of one-dimensional discrete Fourier transforms
Forward transform
The sequence of x(n) is given by x(n) = { x0,x1,x2,… xN-1}.
X(k) = (n=0 to N-1) x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1
Reverse transforms
X(n) = (1/N) (k=0 to N-1) x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1
26. Properties of twiddle factor.
1. Periodicity
WN^(K+N)= WN^K
2. Symmetry
WN^(K+N/2)= -WN^K
27. Give the Properties of one-dimensional DFT
1. The DFT and unitary DFT matrices are symmetric.
2. The extensions of the DFT and unitary DFT of a sequence and their
inverse transforms are periodic with period N.
3. The DFT or unitary DFT of a real sequence is conjugate symmetric
about N/2.
28. Give the Properties of two-dimensional DFT
1. Symmetric
2. Periodic extensions
3. Sampled Fourier transform
4. Conjugate symmetry.
29. What is cosine transform?
The NXN cosine transform c(k) is called the discrete cosine transform and is defined as
C(k) = 1/ N , k=0, 0 n N-1
= (2/N) cos (pi (2n+1)/2N 1 k N-1, 0 n N-1
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30. What is sine transform?
The NXN sine transform matrix = (k,n) also called the discrete sine transform , is
defined as
(k,n) = (2/N+1) sin [ pi* (k+1) (n+1) / (N+1)] , 0 k, n N-1
31. Write the properties of cosine transform:
1) Real & orthogonal.
2) Fast transform.
3) Has excellent energy compaction for highly correlated data
32. Write the properties of sine transform:
1) Real, symmetric and orthogonal.
2) Not the imaginary part of the unitary DFT.
3) Fast transform.
33. Write the properties of Hadamard transform
1) Hadamard transform contains any one value.
2) No multiplications are required in the transform calculations.
4) The no: of additions or subtractions required can be reduced from N^2 to about
Nlog2N
5) Very good energy compaction for highly correlated images.
34 Define Haar transform:
The Haar functions are defined on a continuous interval Xe [0,1] and for K=0,1, N-1
where N=2^n.. The integer k can be uniquely decomposed as K=2^P+Q-1.
35. Write the expression for Hadamard transforms
Hadamard transform matrices Hn are NXN matrices where N=2^n , n= 1,2,3,… is
defined as Hn= Hn-1 * H1 = H1* Hn-1
= 1/ 2 Hn-1 Hn-1
Hn-1 Hn-1
H2 = 1 1
1 –1
36. What are the properties of Haar transform.
1. Haar transform is real and orthogonal.
2. Haar transform is a very fast transform
3. Haar transform has very poor energy compaction for images
4. The basic vectors of Haar matrix sequensly ordered.
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37. What are the Properties of Slant transform
1. Slant transform is real and orthogonal.
2. Slant transform is a fast transform
3. Slant transform has very good energy compaction for images
4. The basic vectors of Slant matrix are not sequensely ordered.
38. Define of KL Transform
KL Transform is an optimal in the sense that it minimizes the mean square error
between the vectors X and their approximations X^. Due to this idea of using the Eigen
vectors corresponding to largest Eigen values. It is also known as principal component
transform.
39. Justify that KLT is an optimal transform.
Since mean square error of reconstructed image and original image is minimum and the
mean value of transformed image is zero so that uncorrelated.
40. What is Image Enhancement?
Image enhancement is to process an image so that the output is more suitable
for specific application.
41. Name the categories of Image Enhancement and explain?
The categories of Image Enhancement are
1. Spatial domain
2. Frequency domain
Spatial domain: It refers to the image plane, itself and it is based on direct
manipulation of pixels of an image.
Frequency domain techniques are based on modifying the Fourier transform of an
image.
42. What do you mean by Point processing?
Image enhancement at any Point in an image depends only on the gray level at
that point is often referred to as Point processing.
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43. Explain Mask or Kernels?
A Mask is a small two-dimensional array, in which the value of the mask
coefficient determines the nature of the process, such as image sharpening.
44. What is Image Negatives?
The negative of an image with gray levels in the range [0, L-1] is obtained by
using the negative transformation, which is given by the expression.
s = L-1-r
Where s is output pixel
r is input pixel
456. Define Histogram?
The histogram of a digital image with gray levels in the range [0, L-1] is a discrete
function h (rk) = nk, where rk is the kth gray level and nk is the number of pixels in the
image having gray level rk.
46. Define Derivative filter?
For a function f (x, y), the gradient f at co-ordinate (x, y) is defined as the vector
f = f/ x
f/ y
f = mag ( f) = {[( f/ x) 2 +( f/ y) 2 ]} 1/2
47. Explain spatial filtering?
Spatial filtering is the process of moving the filter mask from point to point in an
image. For linear spatial filter, the response is given by a sum of products of the filter
coefficients, and the corresponding image pixels in the area spanned by the filter mask.
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48. Define averaging filters?
The output of a smoothing, linear spatial filter is the average of the pixels
contained in the neighborhood of the filter mask. These filters are called averaging
filters.
49. What is a Median filter?
The median filter replaces the value of a pixel by the median of the gray levels in
the neighborhood of that pixel.
50. What is maximum filter and minimum filter?
The 100th percentile is maximum filter is used in finding brightest points in an
image. The 0th percentile filter is minimum filter used for finding darkest points in an
image.
51. Define high boost filter?
High boost filtered image is defined as
HBF= A (original image)-LPF
= (A-1) original image + original image –LPF
HBF= (A-1) original image +HPF
52. State the condition of transformation function s=T(r)
1. T(r) is single-valued and monotonically increasing in the interval 0 r 1 and
2. 0 T(r) 1 for 0 r 1.
53. Write the application of sharpening filters?
1. Electronic printing and medical imaging to industrial application
2. Autonomous target detection in smart weapons.
54. Name the different types of derivative filters?
1. Perwitt operators
2. Roberts cross gradient operators
3. Sobel operators.
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55. Define Restoration?
Restoration is a process of reconstructing or recovering an image that has been
degraded by using a priori knowledge of the degradation phenomenon. Thus restoration
techniques are oriented towards modeling the degradation and applying the inverse
process in order to recover the original image.
56. How a degradation process id modeled?
A system operator H, which together with an additive white noise term (x,y) a
operates on an input image f(x,y) to produce a degraded image g(x,y).
57. What is homogeneity property and what is the significance of this property?
H [k1f1(x,y)] = k1H[f1(x,y)]
Where H=operator
K1=constant
f(x,y)=input image.
It says that the response to a constant multiple of any input is equal to the response to
that input multiplied by the same constant.
58. What is fredholm integral of first kind?

g(x,y) = f(
, )h(x,
,y, )d
d

which is called the superposition or convolution or fredholm integral of first kind. It states
that if the response of H to an impulse is known, the response to any input f(
, ) can be
calculated by means of fredholm integral.
g(x,y)
(x,y)
H
f(x,y)
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59. Define circulant matrix?
A square matrix, in which each row is a circular shift of the preceding row and the
first row is a circular shift of the last row, is called circulant matrix.
Example:
he(o) he(M-1) he(M-2)………… he(1)
he(1) he(0) he(M-1)………. he(2)
He = .
.
.
he(M-1) he(M-2) he(M-3)………. he(0)
60. What is the concept behind algebraic approach to restoration?
Algebraic approach is the concept of seeking an estimate of f, denoted f^, that
minimizes a prefined criterion of performance where f is the image.
61. Why the image is subjected to wiener filtering?
This method of filtering consider images and noise as random process and the
objective is to find an estimate f^ of the uncorrupted image f such that the mean square
error between them is minimized. So that image is subjected to wiener filtering to
minimize the error.
62. Define spatial transformation?
Spatial transformation is defined as the rearrangement of pixels on an image
plane.
63. Define Gray-level interpolation?
Gray-level interpolation deals with the assignment of gray levels to pixels in the
spatially transformed image.
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64. Give one example for the principal source of noise?
The principal source of noise in digital images arise image acquisition
(digitization) and/or transmission. The performance of imaging sensors is affected by a
variety of factors, such as environmental conditions during image acquisition and by the
quality of the sensing elements. The factors are lig the viewer. For example: Contrast Stretching.
Where as Removal of image blur by applying a deblurrings function is considered
a restoration technique.
72. What is segmentation?
The first step in image analysis is to segment the image. Segmentation
subdivides an image into its constituent parts or objects.
73. Write the applications of segmentation.
(i) Detection of isolated points.
(ii) Detection of lines and edges in an image.
74. What are the three types of discontinuity in digital image?
Points, lines and edges.
75. How the discontinuity is detected in an image using segmentation?
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(i) Compute the sum of the products of the coefficient with the gray levels contained in
the region encompassed by the mask.
(ii) The response of the mask at any point in the image is
R = w1z1+ w2z2 + w3z3 +………..+ w9z9
Where zi = gray level of pixels associated with mass coefficient wi.
(iii) The response of the mask is defined with respect to its center
location.
76. Why edge detection is most common approach for detecting discontinuities?
The isolated points and thin lines are not frequent occurrences in most practical
applications, so edge detection is mostly preferred in detection of discontinuities.
77, How the derivatives are obtained in edge detection during formulation?
The first derivative at any point in an image is obtained by using the magnitude of
the gradient at that point. Similarly the second derivatives are obtained by using the
laplacian.
78. Write about linking edge points.
The approach for linking edge points is to analyse the characteristics of pixels in a
small neighborhood (3x3 or 5x5) about every point (x,y)in an image that has undergone
edge detection. All points that are similar are linked, forming a boundary of pixels that
share some common properties.
79. What are the two properties used for establishing
similarity of edge pixels?
(1) The strength of the response of the gradient operator used to produce the edge
pixel.
(2) The direction of the gradient.
W1 W2 W3
W4 W5 W6
W7 W8 W9
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80. Explain about gradient operator.
- The gradient of an image f(x,y) at location (x,y) is the vector
f = GX = f/ x
GY f/ y
-The gradient vector points are in the direction of maximum rate of change of f at (x,y)
- In edge detection an important quantity is the magnitude of this veents?
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The three principal pattern arrangements are vectors, Strings and trees. Pattern
vectors are represented by old lowercase letters such as x y z and in
In the form
x=[x1, x2, ……….., xn ] Each component x represents I th descriptor and n is
the number of such descriptor.
86. What is Data Compression?
Data compression requires the identification and extraction of source redundancy. In
other words, data compression seeks to reduce the number of bits used to store or
transmit information.
87. What are two main types of Data compression?
• Lossless compression can recover the exact original data after compression. It is
used mainly for compressing database records, spreadsheets or word
processing files, where exact replication of the original is essential.
• Lossy compression will result in a certain loss of accuracy in exchange for a
substantial increase in compression. Lossy compression is more effective when
used to compress graphic images and digitised voice where losses outside visual
or aural perception can be tolerated.
88. What is the Need For Compression?
In terms of storage, the capacity of a storage device can be effectively increased with
methods that compress a body of data on its way to a storage device and
decompresses it when it is retrieved.
In terms of communications, the bandwidth of a digital communication link can be
effectively increased by compressing data at the sending end and decompressing data
at the receiving end.
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At any given time, the ability of the Internet to transfer data is fixed. Thus, if data can
effectively be compressed wherever possible, significant improvements of data
throughput can be achieved. Many files can be combined into one compressed
document making sending easier.
89. What are different Compression Methods?
Run Length Encoding (RLE)
Arithmetic coding
Huffman coding and
Transform coding
90. What is run length coding?
Run-length Encoding, or RLE is a technique used to reduce the size of a repeating
string of characters. This repeating string is called a run; typically RLE encodes a run of
symbols into two bytes, a count and a symbol. RLE can compress any type of data
regardless of its information content, but the content of data to be compressed affects
the compression ratio. Compression is normally measured with the compression ratio:
91. Define compression ratio.
Compression Ratio = original size / compressed size: 1
92. Give an example for Run length Encoding.
Consider a character run of 15 'A' characters, which normally would require 15 bytes
to store:
AAAAAAAAAAAAAAA coded into 15A
With RLE, this would only require two bytes to store; the count (15) is stored as the first
byte and the symbol (A) as the second byte.
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93. What is Huffman Coding?
Huffman compression reduces the average code length used to represent the symbols
of an alphabet. Symbols of the source alphabet, which occur frequently, are assigned
with short length codes. The general strategy is to allow the code length to vary from
character to character and to ensure that the frequently occurring characters have
shorter codes.
94. What is Arithmetic Coding?
Arithmetic compression is an alternative to Huffman compression; it enables characters
to be represented as fractional bit lengths. Arithmetic coding works by representing a
number by an interval of real numbers greater or equal to zero, but less than one. As a
message becomes longer, the interval needed to represent it becomes smaller and
smaller, and the number of bits needed to specify it increases.
95. What is JPEG?
The acronym is expanded as "Joint Photographic Expert Group". It is an international
standard in 1992. It perfectly Works with colour and greyscale images, Many
applications e.g., satellite, medical,...
96. What are the basic steps in JPEG?
The Major Steps in JPEG Coding involve:
DCT (Discrete Cosine Transformation)
Quantization
Zigzag Scan
DPCM on DC component
RLE on AC Components
Entropy Coding
97. What is MPEG?
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The acronym is expanded as "Moving Picture Expert Group". It is an international
standard in 1992. It perfectly Works with video and also used in teleconferencing
98. What is transform coding?
Transform coding is used to convert spatial image pixel values to transform coefficient
values. Since this is a linear process and no information is lost, the number of
coefficients produced is equal to the number of pixels transformed.
The desired effect is that most of the energy in the image will be contained in a few
large transform coefficients. If it is generally the same few coefficients that contain most
of the energy in most pictures, then the coefficients may be further coded by loss less
entropy coding. In addition, it is likely that the smaller coefficients can be coarsely
quantized or deleted (lossy coding) without doing visible damage to the reproduced
image.
99. What are the different transforms used in transform coding and how the
differ?
Many types of transforms used for picture coding, are Fourier, Karhonen-Loeve, Walsh-
Hadamard, lapped orthogonal, discrete cosine (DCT), and recently, wavelets. The
various transforms differ among themselves in three basic ways that are of interest in
picture coding:
1) The degree of concentration of energy in a few coefficients;
2) The region of influence of each coefficient in the reconstructed picture;
3) The appearance and visibility of coding noise due to coarse quantization of the
coefficients.
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100. Draw the JPEG Encoder.
101. Draw the JPEG Decoder.
102. What is zig zag sequence?
The purpose of the Zig-zag Scan:
To group low frequency coefficients in top of vector.
Maps 8 x 8 to a 1 x 64 vector
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103.Explain the term digital image.
The digital image is an array of real or complex numbers that is represented by a finite no
of bits.
104.Write any four applications of DIP.
i. Remote sensing
ii. Image transmission and storage for business application
iii. Medical imaging
iv. Astronomy
105.What is the effect of Mach band pattern.
The intensity or the brightness pattern perceive a darker stribe in region D and brighter
stribe in region B.This effect is called Mach band pattern or effect.
106.Find the number of bits to store a 128 128 image with 64 gray levels.
Given:
M = N = 128
L = 64 =2k
=> k=6
No. of bits = M2k
= 1282*6
= 98304 bits
107.Name the types of connectivity and explain
a. 4-connectivity:
Two pixels p and q with values from V are 4-connected if q is in the set N4(p)
b. 8- connectivity:
Two pixels p and q with values from V are 8-connected if q is in the set N8(p)
c. m- connectivity:
Two pixels p and q with values from V are m-connected if
i. q is in N4(p) or
ii. q is in ND(p) and the set N4(p) N4(q) =
108.Define the chessboard distance
It is also known as D8 distance given by
D8 (p,q) = max( x-s , y-t )
The pixels with D8 distance from (x,y) less than or equal to some value r form a square centered
at (x,y).
109.Write down the properties of 2D fourier transform.
• Separability
• Translation
• Periodicity and Conjugate property
• Rotation
• Distributivity and scaling
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• Average value
• Convolution and Correlation
• Laplacian
•
110.Obtain the Hadamard transformation for N = 4
N = 4 = 2n
=> n = 2
111.Write down the properties of Haar transform.
• Real and orthogonal
• Very fast transform
• Basis vectors are sequentially ordered
• Has fair energy compaction for image
• Useful in feature extraction,image coding and image analysis problem
•
112.What is enhancement.
Image enhancement is a technique to process an image so that the result is more suitable
than the original image for specific applications;
113.What is point processing.
Enhancement at any point in an image depends only on the gray level at that point is
referred to as point processing.
114.What is gray level slicing.
Highlighting a specific range of gray levels in an image is referred to as gray level
slicing.It is used in satellite imagery and x-ray images
115.What is histogram equalization
It is a technique used to obtain linear histogram . It is also known as histogram
linearization.Condition for uniform histogram is
Ps(s) = 1
116.Discuss the Roberts cross-gradient operators.
Using cross difference
f = |z5-z9|+|z6-z8|
f can be implemented by 2 2 mask
x
u
0 1 2 3
0 + + + +
1 + + + +
2 + + - -
3 + + - -
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0 1
-1 0
This is called as Roberts cross gradient operator
117.Define the degradation phenomena.
Image restoration or degradation is a process that attempts to reconstruct or recover an
image that has been degraded by using some clear knowledge of the degradation
phenomena.Degradation may be in the form of
• Sensor noise
• Blur due to camera misfocus
• Relative object camera motion
•
118.What is unconstrained restoration.
It is also known as least square error approach.
n = g-Hf
To estimate the original image f^,noise n has to be minimized and
f^ = g/H
119.Draw the image observation model.
120.What is blind image restoration
Degradation may be difficult to measure or may be time varying in an unpredictable
manner. In such cases information about the degradation must be extracted from the observed
image either explicitly or implicitly. This task is called blind image restoration.
1 0
0 -1
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16 marks:-
1.Explain various functional block of digital image processing
Hint:
Block diagram and explain about each blocks (Image acquisition, enhancement,
restoration, color image, wavelets, compression, segmentation, representation & description,
recognition).
2.Briefly explain the elements of human visual system
Hint:
Diagram-Structure of human eye
Three membranes-cornea,sclera,choroids;Lens;Retina-Cones,rods;Blind spot;Fovea
3.Describe image formation in the eye with brightness adaptation and discrimination
Hint:
Brightness adaptation-large variation of intensity by changes in its overall sensitivity
.Subjective brightness,Weber ratio,Mach band effect ,simultaneous contrast
4.Explain inroperties
9.Define Haar transform.Derive the same for n=8.What are its properties
Hint:
Based on haar function hk (z) defined over z (0, 1)
K=2p+q-1
Hk (z) = (1/ N )2p/2 , (q-1)/2p Z (q-1/2)/2p
= (1/ N )-2p/2 , (q-1/2)/2p Z q/2p
=0 , otherwise
And properties
10.Discuss the properties and applications of 1)Hadamard transform 2)Hotelling transform
Hint:
Properties of hadamard:
Real and orthogonal
fast transform
faster than sine transform
Good energy compaction for image
Appl:
Image data compression, filtering and design of course
Properties of hotelling:
Real and orthogonal
Not a fast transform
Best energy compaction for image
Appl:
Useful in performance evaluation & for finding performance bounds
11.Discuss the image smoothing filter with its model in the spatial domain.
Hint:
LPF-blurring
Median filter – noise reduction & for sharpening image
12.What are image sharpening filters.Explain the various types of it.
27
Hint:
used for highlighting fine details
HPF-output gets sharpen and background becomes darker
High boost- output gets sharpen but background remains unchanged
Appl:
Medical image,electronic printing,industrial inspection
13.Discuss in detail about homomorphic & derivative filters.
Hint:
Homomorphic:Improving the appearance of an image by simultaneous compression and
contrast enhancement.
f(x,y)= i(x,y)r(x,y)
block diagram
Derivative:To obtain more sharpened image
Roberts cross gradient operator ,prewitt operator, sobel operator
14.Explain Weiner smoothing filter and its relation with inverse filtering and diffracted
limited systems.
Hint:
Weiner filter: Mean square error
e
2=E{[U(m,n)-Û(m,n)]2}

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